Computational Optimization and Applications

, Volume 62, Issue 1, pp 291–321 | Cite as

Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

Article

Abstract

We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau–Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented to illustrate the effectiveness of the adaptivity for both regularization techniques.

Keywords

Optimal control problem State constraints Discontinuous Galerkin methods Convection diffusion equations  A posteriori error estimates 

Notes

Acknowledgments

The authors would like to thank Martin Stoll for helpful discussions about this research. This work was supported by the Forschungszentrum Dynamische Systeme (CDS): Biosystemtechnik, Otto-von-Guericke-Universität Magdeburg. The authors also would like to express their sincere thanks to the referees for most valuable suggestions.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Computational Methods in Systems and Control TheoryMax Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany

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